Multiple choice

The ratio of A's age 3 years ago and B's age 5 years hence is 3: 4. The average of the ages of A and C is 20 years. Also C's age after 10 years will be 2 more than twice the present age of B. Find the age of C.

  1. 22 years

  2. 24 years

  3. 15 years

  4. 18 years

  5. None of these
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A Correct answer
Explanation

Let A's present age = A, B's present age = B, C's present age = C. Given: (A-3)/(B+5) = 3/4, (A+C)/2 = 20, C+10 = 2B+2. From second eq: A+C=40, so A=40-C. From third eq: C = 2B - 8. Substitute in first: (40-C-3)/(B+5) = 3/4. Using C=2B-8: (40-2B+8-3)/(B+5) = 3/4, so (45-2B)/(B+5) = 3/4. Cross-multiply: 180-8B = 3B+15, so 165 = 11B, B = 15. Then C = 2(15)-8 = 22 years (option A).

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